Irrigation Calculation: Culturable Command Area (CCA)

This solution explains the calculation of the Culturable Command Area (CCA) using the provided details about tubewell discharge and irrigation practices.

Calculate Daily Water Supply

The tubewell discharges water at a rate of $25 \text{ m}^3/\text{h}$ and operates for $10$ hours daily.

The total daily discharge is:

$ \text{Daily Discharge} = 25 \frac{\text{m}^3}{\text{h}} \times 10 \text{ h} = 250 \text{ m}^3/\text{day} $

Determine Water Supplied Over Irrigation Interval

The irrigation interval is given as $20$ days. The total water supplied by the tubewell during this period is:

$ \text{Total Supply (20 days)} = 250 \frac{\text{m}^3}{\text{day}} \times 20 \text{ days} = 5000 \text{ m}^3 $

Calculate Water Required for Irrigation

The average irrigation depth is $80 \text{ mm}$, which converts to $0.080 \text{ m}$. The intensity of irrigation is $80\%$ ($0.80$).

Let CCA represent the Culturable Command Area in hectares.

The actual area irrigated is $0.80 \times \text{CCA}$ hectares.

Convert the irrigated area to square meters:

$ \text{Irrigated Area (m}^2\text{)} = (0.80 \times \text{CCA}) \text{ ha} \times 10000 \frac{\text{m}^2}{\text{ha}} = 8000 \times \text{CCA} \text{ m}^2 $

The volume of water needed for this irrigation is:

$ \text{Volume Required} = \text{Irrigated Area (m}^2\text{)} \times \text{Irrigation Depth (m)} $

$ \text{Volume Required} = (8000 \times \text{CCA}) \text{ m}^2 \times 0.080 \text{ m} = 640 \times \text{CCA} \text{ m}^3 $

Calculate Culturable Command Area (CCA)

Equate the total water supplied over the 20-day interval to the volume required for irrigation:

$ \text{Total Supply (20 days)} = \text{Volume Required} $

$ 5000 \text{ m}^3 = 640 \times \text{CCA} \text{ m}^3 $

Solve for CCA:

$ \text{CCA} = \frac{5000}{640} $

$ \text{CCA} = \frac{500}{64} = \frac{125}{16} = 7.8125 \text{ hectares} $

Rounded to two decimal places, the CCA is $7.81$ hectares.